Question

A parallelogram has a base of 2cm and a height of 9cm. A triangle has a base of 6cm and a height of 6cm. Which statement is TRUE?(1 point)
Responses

The parallelogram has a greater area.
The parallelogram has a greater area.

The triangle has a greater area.
The triangle has a greater area.

Both shapes have the same area.

Answer 1

To determine which shape has a greater area, we can calculate the area of each shape using the following formulas:

1. **Area of a parallelogram**:
\[
\text{Area} = \text{base} \times \text{height}
\]
For the parallelogram:
\[
\text{Area} = 2 \, \text{cm} \times 9 \, \text{cm} = 18 \, \text{cm}^2
\]

2. **Area of a triangle**:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
For the triangle:
\[
\text{Area} = \frac{1}{2} \times 6 \, \text{cm} \times 6 \, \text{cm} = \frac{1}{2} \times 36 \, \text{cm}^2 = 18 \, \text{cm}^2
\]

Now we compare the areas:
- Area of the parallelogram: \( 18 \, \text{cm}^2 \)
- Area of the triangle: \( 18 \, \text{cm}^2 \)

Both shapes have the same area.

Thus, the correct statement is: **Both shapes have the same area.**